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e c o l o g i c a l m o d e l l i n g 1 9 9 ( 2 0 0 6 ) 132–141
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Effects of sample survey design on the accuracy of
classification tree models in species
distribution models
Thomas C. Edwards Jr. a,∗ , D. Richard Cutler b , Niklaus E. Zimmermann c ,
Linda Geiser d , Gretchen G. Moisen e
a
USGS Utah Cooperative Fish and Wildlife Research Unit, College of Natural Resources,
Utah State University, Logan, UT 84322-5290, USA
b Department of Mathematics and Statistics, Utah State University, Logan, UT 84322-3900, USA
c Department of Landscape Research, Swiss Federal Research Institute WSL, Zuercherstrasse 111, CH-8903 Birmensdorf, Switzerland
d USDA Forest Service, Siuslaw National Forest, P.O. Box 1148, Corvallis, OR 97339, USA
e USDA Forest Service, Rocky Mountain Research Station, 507 25th Street, Ogden, UT 84401, USA
a r t i c l e
i n f o
a b s t r a c t
Article history:
We evaluated the effects of probabilistic (hereafter DESIGN) and non-probabilistic (PURPO-
Published on line 24 July 2006
SIVE) sample surveys on resultant classification tree models for predicting the presence of
four lichen species in the Pacific Northwest, USA. Models derived from both survey forms
Keywords:
were assessed using an independent data set (EVALUATION). Measures of accuracy as gauged
Model accuracy
by resubstitution rates were similar for each lichen species irrespective of the underlying
Sample survey
sample survey form. Cross-validation estimates of prediction accuracies were lower than
Study design
resubstitution accuracies for all species and both design types, and in all cases were closer
Classification trees
to the true prediction accuracies based on the EVALUATION data set. We argue that greater
Lichens
emphasis should be placed on calculating and reporting cross-validation accuracy rates
Accuracy assessment
rather than simple resubstitution accuracy rates. Evaluation of the DESIGN and PURPOSIVE
Probability samples
tree models on the EVALUATION data set shows significantly lower prediction accuracy for
Non-probability samples
the PURPOSIVE tree models relative to the DESIGN models, indicating that non-probabilistic
sample surveys may generate models with limited predictive capability. These differences
were consistent across all four lichen species, with 11 of the 12 possible species and sample survey type comparisons having significantly lower accuracy rates. Some differences in
accuracy were as large as 50%. The classification tree structures also differed considerably
both among and within the modelled species, depending on the sample survey form. Overlap in the predictor variables selected by the DESIGN and PURPOSIVE tree models ranged
from only 20% to 38%, indicating the classification trees fit the two evaluated survey forms
on different sets of predictor variables. The magnitude of these differences in predictor variables throws doubt on ecological interpretation derived from prediction models based on
non-probabilistic sample surveys.
© 2006 Elsevier B.V. All rights reserved.
∗
Corresponding author at: USGS Utah Cooperative Research Unit, 5290 Old Main Hill, Utah State University, Logan, UT 84322-5290, USA.
Tel.: +1 435 797 2529; fax: +1 435 797 4025.
E-mail address: [email protected] (T.C. Edwards Jr.).
0304-3800/$ – see front matter © 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.ecolmodel.2006.05.016
e c o l o g i c a l m o d e l l i n g 1 9 9 ( 2 0 0 6 ) 132–141
1.
Introduction
Species distribution models rely heavily on the collection of
site-specific data from the hypothesized spatial and environmental ranges of target species. Once the data are collected, many different types of analytical methods can be used
to ascertain relationships between measured environmental
variables and species occurrence. One of the more common
forms of analysis applied to data of this type is that of classification models, which are used to discriminate between nominal response values using a set of environmental predictors.
Applications of classification models to species distribution
modelling abound in the published literature, and range from
predicting the distribution or characteristics of plant species
(Austin et al., 1983, 1990; Frescino et al., 2001; Zimmermann
and Kienast, 1999) to habitat relationships of terrestrial animal species (McNoleg, 1996; Jaberg and Guisan, 2001; Lawler
and Edwards, 2002; Welch and MacMahon, 2005). An excellent
overview of the state of species distribution modelling can be
found in Scott et al. (2002).
Classification models can be created using various statistical approaches, including generalized linear models (GLM)
(McCullagh and Nelder, 1989) such as logistic regression
(Hosmer and Lemeshow, 2000), generalized additive models
(GAM) (Hastie and Tibshirani, 1990; Yee and Mitchell, 1991),
which are semi-parametric extensions of GLMs, and fully nonparametric methods such as classification trees (Breiman et
al., 1984; De’ath and Fabricius, 2000). The latest generation of
statistical classification procedures, including support vector
machines, random forests (Breiman, 2001), and other ensemble classifiers (Steele, 2000), have strong potential for ecological classification but have not yet received much attention.
Irrespective of the selected analytical methodology, the ecological object to be modelled – be it species presence, or some
attribute of species presence such as a bird nesting site or habitat use – is typically surveyed, and a response, often nominal,
is tallied and linked with a set of ecological predictor variables.
Depending on the analytical method, the predictors can be
nominal, ordinal, ratio, or interval scales, or mixtures of both.
Data for species distribution modelling are typically
obtained by survey sampling. Ideally, survey sampling involves
the random selection and measurement of samples from a
defined, target population referred to as the sampling frame.
Sampling frames can have many different characteristics.
Often sampling frames are a defined spatial extent, considered a finite population, that is divided into N smaller units of
some set size, from which a subset ni is randomly selected and
surveyed for the species of interest (see Edwards et al., 2004).
These area samples (sensu Nusser et al., 1998) may, or may not,
correspond with the actual sample unit, which may be something as simple as the presence or absence of a specific species
within the area being sampled. Estimates derived from these
types of sampling designs are considered design-based, and
carry with them the power of inferential statistics.
Many ecological studies, however, deal with attempts to
survey and build a classification model for ecological events
best described as rare or uncommon on the landscape (Engler
et al., 2004; Edwards et al., 2005). Rare ecological events may
not be truly amenable to randomization procedures per se,
133
especially when the goal is to generate sufficient observations
for a classification model (see Edwards et al., 2005). For example, the random selection of small areas within some defined
spatial extent like a conservation reserve, which is then surveyed to locate bird nests, might not be a fruitful exercise if too
few bird nests are found. While such a design would allow for
inferential statistics to be determined for, say percent of sites
occupied (see Edwards et al., 2004), it may not provide sufficient tallies of nest presence, thereby precluding attempts
to build a classification model. Consequently, ecologists often
actively search for the event of interest using non-probability
sampling procedures (see Cochran, 1977). One of the more
common of these non-probability sampling efforts, termed
purposive sampling, occurs when ecologists actively seek the
event of interest, such as an active breeding nest of a bird, or
a specific plant species.
Our objective was to compare classification models that
predict the presence of four lichens common in the Pacific
Northwest, USA. These models were developed from environmental data collected from randomly versus purposively
selected sample sites. We specifically evaluated two common sample designs used to collect the model building data;
the first used presence–absence data collected on a randomly started, systematic grid. Such probability-based sampling efforts support design-based inference (see Gregoire,
1998), and are the basis of many current efforts to model
and assess environmental and ecological systems (Olsen and
Schreuder, 1997; Olsen et al., 1999). The second set of models was based on presence–absence data collected in a nonprobability, or purposive, framework, where biologists used
knowledge of lichen life histories to search for and “sample” for lichen presences. Unlike probabilistic samples, those
collected in a purposive framework can have questionable
inference, due principally to biases associated with the nonrandom selection of sample locations. Identical predictor variables were used for both sample design forms, allowing us to
test whether the probability-based and purposive sampling
resulted in the same final models. An independent data set
was collected using probability sampling as well and used for
validation. Effects of the two sample designs were evaluated by
various measures of model accuracy and fit, and by performing both internal cross-validation and external, independent
validation exercises. All data were collected in the same spatial area.
2.
Methods
2.1.
Study design and species
Data used in our analyses were collected from seven national
forests and adjacent Bureau of Land Management (BLM) districts in the Cascades and Coast Ranges of Oregon and Washington (Fig. 1). All sample sites in the study region were surveyed at least once as part of a broader effort using epiphytic
macrolichens as indicators of air quality (Geiser, 2004). Four
¨
common lichen species, Lobaria oregana (Tuck.) Mull.,
L. pulmonaria (L.) Hoffm., Pseudocyphellaria anomala Brodo & Ahti,
and P. anthraspis (ACH.) H. Magn., were used in the analyses
presented here. Each of these four species had sufficient num-
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e c o l o g i c a l m o d e l l i n g 1 9 9 ( 2 0 0 6 ) 132–141
Fig. 1 – Depiction of the Northwest Forest Plan study region,
Pacific Northwest, USA. Sample regions for the DESIGN,
PURPOSIVE and EVALUATION study areas are in black. Note
on inset the regularity of the DESIGN and EVALUATION
sample plots, and the clumped nature of the PURPOSIVE
plots.
bers of detections (>50) for developing the models used in our
comparisons. All four species are large, foliose, broadly distributed cyanolichens that can be found on tree trunks, live
branches, and leaf litter of conifers of the Pacific Northwest.
All achieve their greatest biomass in riparian and late-seral
forests. Eye-level habitat and large size makes them relatively
easy to find and identify.
Two sample surveys common to predictive models in
ecology were evaluated. The first (hereafter DESIGN) was a
probability-based sampling effort. The DESIGN survey used
data collected on the Current Vegetation Survey plots (CVS),
a randomly started, systematic ∼5.47 km grid overlaid on all
Forest Service and BLM lands in the Pacific Northwest. Its
principal application is the generation of estimates of forest
resources (see Max et al., 1996). Sites were surveyed by field
botanists trained and certified in the recognition and differentiation of regional epiphytic macrolichens.
The second survey was purposive, a non-probability design
where samples are searched for and collected based on a
desired need or outcome (hereafter PURPOSIVE). Its common
use in ecological studies reflects the reality of ecological modelling exercises involving rare or uncommon events, such as
the presence of a bird nest (e.g., Lawler and Edwards, 2002)
or a plant species (e.g., Dreisbach et al., 2002). Because the
survey sites were not randomly selected, introduced bias is a
concern. Here, field botanists essentially searched for lichens
using no underlying sample design, relying instead on their
personal knowledge of lichen life history to guide their sampling efforts on the landscape. The botanists were searching
for targeted lichen species in areas proposed for timber harvest or other management actions on public lands.
The third sampling effort (hereafter EVALUATION) was
probability-based, and served as an independent test data
set for the DESIGN and PURPOSIVE models. The EVALUATION surveys covered national forests and BLM districts in
three regions of the Pacific Northwest, including the southern Washington Cascades, the Oregon Coast Range, and the
Umpqua Basin. Within each of the three areas a stratified
random sample of sites on a randomly started ∼2.7 km grid
was obtained. The stratification criteria were reserve status
(reserve and non-reserve) and age class (<80 and 80 + years) of
the dominant tree species. Allocations to the four strata were
60% to reserve/80+, 20% to reserve/<80, and 10% to each of
the non-reserve strata. These allocations reflected the priorities of a different research effort (see Edwards et al., 2005), but
are essentially a proportional allocation for the EVALUATION
study region.
A total of 840 plots were sampled in the DESIGN, and 299
in the PURPOSIVE effort. These two data sets constituted the
training data. An additional 300 sites were surveyed in the
EVALUATION design for model assessment purposes. To alleviate concern over the possible effects of the different sample
sizes between the DESIGN and PURPOSIVE data sets, we randomly selected 100 samples of size 299 from the DESIGN data,
fit a classification tree for the lichen species on each of these
subsets, and predicted the occurrence of the lichen species
both on the data sets of size 299 on which they were fit and for
the EVALUATION data. Mean differences across all evaluation
metrics (see below) ranged from 2.8% to 2.1%, well within any
binomial error range and indicative of no sample size effect
on our results.
Presence and absence of each lichen species was recorded
on a 0.4 ha plot centered on the central (#1) subplot on each
CVS site for the DESIGN surveys (details in Edwards et al.,
2004). Plot size for the EVALUATION surveys was smaller, only
0.2 ha in size. Plot size for the PURPOSIVE surveys was variable according to the size of the proposed sale or management action. If the purpose of our study was to compare
the estimated percent occupancy rates from the DESIGN and
PURPOSIVE surveys versus the EVALUATION survey, the difference in the size of the sample units would be a concern
given that larger plots will have higher probabilities of occupancy. However, the purpose of our analyses is to use the
DESIGN and PURPOSIVE data to fit models predicting the likelihood of occurrence of the four identified lichen species,
and the EVALUATION data for assessment. For this application it does not matter if the EVALUATION plot size is the
same, larger, or smaller than the DESIGN and PURPOSIVE plot
size.
e c o l o g i c a l m o d e l l i n g 1 9 9 ( 2 0 0 6 ) 132–141
135
Both the DESIGN and PURPOSIVE training data sets were colocated in the Cascade Mountains of Oregon and Washington,
while the independent EVALUATION data set was collected
in the Oregon Coastal Range (Fig. 1). The EVALUATION data
set was not co-located in the same spatial extent as the two
training data sets to allow for an independent test of model
extrapolative capabilities. All three data sets were within the
known distribution ranges of all four of the surveyed lichens.
of the 11 sets of monthly bio-climatic predictors. In each
case, the first principal component was an average of the
12 monthly measurements, while the second principal component was a contrast of values for 6 so-called summer
months (April–September) to the 6 so-called winter months
(October–March). For each set of 12 monthly variables, these
two principal components explained over 95% of the variability, and in most cases the first two principal components
explained over 99% of the variability in the sets of variables. Accordingly, we defined two new variables for each
set of monthly bio-climatic predictors: (1) the average of the
12 monthly variables; (2) the difference between the sum of
the summer monthly values and the winter monthly values,
divided by 12. Hereafter we use the variable suffix “A” to denote
the average of the 12 monthly measurements, and the suffix
“D” to denote the difference derived variable. Thus, TMINA
is the average minimum temperature for the 12 months and
PRECD is the difference between summer and winter precipitation. See Edwards et al. (2005) for additional specifics on the
derivation of the DAYMET-based bio-climatic variables.
Vegetation variables came from the BLM Interagency Vegetation Mapping Project1 (IVMP) and the USDA Forest Service, Forest Inventory and Analysis program2 (FIA). Variables
from the IVMP were derived from Landsat Thematic Mapper
imagery, and included percent cover of all vegetation, conifer,
and broadleaf species. Maps were obtained at a resolution of
25 m, and were resampled using a bilinear interpolation to
90 m resolution within a GIS. The two vegetation variables
obtained from the FIA were forest type and above ground live
tree biomass, both modelled for the continental US, Alaska,
and Puerto Rico at 250 m resolution. These nationwide maps
were constructed by modeling forest type and biomass collected on FIA sample plots as nonparametric functions of
numerous ancillary predictor layers, including: 16-day Moderate Resolution Imaging Spectrometer (MODIS) composites and
associated vegetation indices and MODIS percent tree cover;
vegetative diversity and type synthesized from the National
Land Cover Dataset; topographic variables derived from Digital Elevation Models; monthly and annual climate parameters;
other ancillary variables (J. Blackard, USFS, personal communication, 2005).
2.2.
2.3.
Table 1 – Topographic, bio-climatic and vegetation
variables used to model the probability of presence for
four lichen species in the study area of the Pacific
Northwest Forest Plan
Variable
type/name
Topographic
SLPE
ASPE
ELEV
Bio-climatic
ETPJ
MIND
PREC
RELH
SFMM
TAVE
TDAY
TMAX
TMIN
VPAM
VPSA
Vegetation
BDLCNT
CNFCNT
FORBIO
VEGCNT
Description
Units
Percent slope
Aspect
Elevation
Percent, 0–90
Degree 0, 1–360
m
Potential
evapotranspiration
Monthly moisture index
Precipitation
Relative humidity
Monthly potential global
radiation
Monthly average
temperature
Monthly average daytime
temperature
Maximum temperature
Minimum temperature
Ambient vapor pressure
Saturated vapor pressure
mm
Percent broadleaf cover
Percent conifer cover
Live tree (>1 in DBH)
biomass, above ground
dry weight
Percent vegation cover
Percent, 0–100
Percent, 0–100
tonnes/acre
cm
cm
Percent
kJ
◦
C
◦
C
◦
C
C
Pa
Pa
◦
Percent, 0–100
Data structure and characteristics
All plot locations were intersected with maps of topographic,
bio-climatic, and vegetation variables (Table 1) in a geographic
information system (GIS). The selected environmental variables were all hypothesized to have direct relationships to the
presence of the modelled lichen species. Ninety meters resolution topographic variables (slope, aspect and elevation) were
obtained by resampling the 30 m resolution National Elevation
Data set (NED) (Gesch et al., 2002).
Bio-climatic variables were derived from the DAYMET
1 km daily-gridded weather surfaces that have been reduced
to 18-year monthly and yearly climatological summaries
(1981–1998) (Thornton et al., 1997; Thornton and Running,
1999). Preliminary analyses showed that correlations among
the monthly values for the 11 sets of bio-climatic predictor variables were high. To address the issue of collinearity,
a principal components analysis was carried out on each
Statistical modelling and assessment
We used classification trees (Breiman et al., 1984) to relate
the DESIGN and PURPOSIVE lichen presences to the modelled
topographic, bio-climatic, and vegetation predictor variables.
We followed the approach suggested by De’ath and Fabricius
(2000), pruning trees by cross-validation and the 1-SE rule. Separate models were built for each species in each of the DESIGN
and PURPOSIVE surveys. We next applied the resultant sampling design (n = 2) and species-specific (n = 4) classification
tree models (total models = 8) to our spatially explicit predictors within the GIS, and modelled the probability of presence
of each of the four lichen species for the EVALUATION sample plots. Observations from the EVALUATION study area were
1
2
http://www.or.blm.gov/gis/projects/vegetation/ivmp.
http://www.fia.fs.fed.us/.
136
e c o l o g i c a l m o d e l l i n g 1 9 9 ( 2 0 0 6 ) 132–141
Fig. 2 – Percent of sample plots at which each lichen
species was present in the DESIGN (n = 840), PURPOSIVE
(n = 299), and EVALUATION (n = 300) study sites, area of the
Pacific Northwest Forest Plan, Pacific Northwest, USA.
Number of detections for each species and sampling form
are shown above each histogram bar.
then compared against the predicted DESIGN and PURPOSIVE
probabilities for that plot, allowing us to link the presence or
absence of each of the four common species to an estimate
of the probability of presence. All trees were fit using the rpart
library of functions in the R statistical package3 (Ihaka and
Gentleman, 1996).
Three general classes of model accuracy were used to
compare the models based on the DESIGN and PURPOSIVE
data. These classes were: (1) resubstitution (model) accuracy
rates for each of the eight models; (2) 10-fold cross-validation
(Manly, 1997) estimates of accuracy for each of the eight models; (3) a prediction accuracy rate for the independent EVALUATION survey, based on a probability of presence threshold of
P > 0.5. Threshold-dependent measures of accuracy reported
and assessed included percent correct classification rate (PCC),
sensitivity, specificity, and kappa (after Fielding and Bell, 1997).
Cut-off for these metrics was assumed to be 0.5. The areas
under the receiver operator characteristic (AUC), plus SE, were
also calculated from formulae provided by Hanley and McNeil
(1982).
3.
Results
L. pulmonaria, P. anomala and P. anthraspis occurred with the
greatest frequency in the PURPOSIVE compared to the DESIGN
and EVALUATION surveys (Fig. 2). L. oregana occurred with the
greatest frequency in the EVALUATION survey, and with similar frequency in the PURPOSIVE and DESIGN surveys.
Classification tree models for the four lichen species ranged
from 88.0% to 91.1% and 83.8% to 92.6% accurate (PCC) for
the DESIGN and PURPOSIVE surveys, respectively (Table 2).
Measures of tree specificity and sensitivity between the survey forms were similar between species, too, indicating that
the trees were maximizing classification to the extent possible
3
http://www.r-project.org/.
given the predicator variables. In short, measures of accuracy
as gauged by resubstitution rates were similar for each species
irrespective of sample survey form.
Cross-validated accuracy estimates were lower for all
species and sampling forms, with percent correct classification rates ranging from 79.7% to 85.6% for the DESIGN and from
55.7% to 78.6% for the PURPOSIVE design (Table 2). As with the
PCC, sensitivities were similar in the magnitude of difference
between the DESIGN and PURPOSIVE, but lower overall relative to PCC. Specificity decreased dramatically when DESIGN
and PURPOSIVE were compared by species. Similar patterns
in decline occurred for kappa and AUC as well.
Tree structure differed considerably both among and
within the modelled species, depending on the sampling form
(Table 3). One indication of this variability in model complexity
is based on the number of levels required to build the trees.
For example, the number of tree levels for L. oregana was 11
for the DESIGN, but only 4 for the PURPOSIVE sampling form.
P. anomala had 10 levels for the DESIGN and 7 for PURPOSIVE.
Both L. pulmonaria and P. anthraspis had 8 and 9, and 7 and 8,
levels for the DESIGN and PURPOSIVE sampling forms, respectively. No real pattern is apparent.
Pattern was lacking in tree variable selection as well. While
differences among the variables used by the tree classifier
were expected among species, the magnitude of differences
in variables used to discriminate presence within a species
varied tremendously by sampling form (Table 3). One indication of this variability is the overlap in tree-selected variables.
Overall, 18 of the 21 tree-selected variables (85.7%) overlapped
among the species and survey forms. However, variable overlap was considerably lower when survey forms were compared
within a species. Overlap based on sampling form was only 3
of 11 (27.3%) for L. oregana, 5 of 13 (38.5%) for L. pulmonaria and
P. anomala, and 3 of 15 (20.0%) for P. anthraspis, indicating the
sampling forms were classifying on different sets of predictor
variables.
Assessment of the DESIGN and PURPOSIVE tree models on
the EVALUATION validation data set shows lower overall prediction accuracy for the PURPOSIVE tree models compared to
DESIGN models (Table 4). This is consistent across all four
lichen species, with 11 of the 12 possible comparisons having significantly lower accuracy rates. Differences in specificity
are particularly large, typically about 50%. Differences in sensitivity are not as severe, but still indicate an overall pattern
of lower accuracy in the PURPOSIVE tree models. Measures of
kappa and AUC were significantly lower for the PURPOSIVE
compared to the DESIGN survey, too.
Resubstitution DESIGN and PURPOSIVE PCC, sensitivity,
and specificity accuracy rates were statistically greater than
the EVALUATION accuracy rates for 36 of 40 possible tests
of species, sampling form and accuracy rates (Table 5). Both
the DESIGN and PURPOSIVE sampling forms consistently overestimated resubstitution accuracy irrespective of the species
and accuracy rate when compared to the independent EVALUATION data. A different pattern emerges when evaluating
cross-validation accuracy rates, where only 12 of 40 possible tests showed difference (Table 6). However, there were
extreme differences among the DESIGN and PURPOSIVE sampling forms, with 10 of 20 possible PURPOSIVE tests indicating
statistical differences between PURPOSIVE cross-validation
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Table 2 – Percent correct classification (PCC), sensitivity and specificity accuracy rates, and kappa and AUC, for the
DESIGN and PURPOSIVE classification tree models of four lichen species in the Pacific Northwest, USA
Species
Survey form
Resubstitution
10-Fold cross-validation
PCC
Specificity
Sensitivity
Kappa
AUC
PCC
Specificity
Sensitivity
Kappa
AUC
L. oregana
DESIGN
PURPOSIVE
88.6
85.6
95.6
95.7
64.2
49.2
0.644
0.515
0.906
0.761
79.2
78.9
88.5
89.7
49.5
40.0
0.368
0.324
0.734
0.601
L. pulminaria
DESIGN
PURPOSIVE
88.0
78.3
93.6
74.7
69.1
83.0
0.650
0.565
0.882
0.721
81.1
52.2
90.6
61.2
49.5
40.3
0.429
0.015
0.788
0.498
P. anomala
DESIGN
PURPOSIVE
90.1
81.6
96.1
93.2
63.2
48.0
0.640
0.462
0.856
0.782
84.2
69.6
93.3
82.4
42.8
32.5
0.403
0.157
0.763
0.532
P. anthraspis
DESIGN
PURPOSIVE
91.1
82.0
97.4
93.2
64.5
51.2
0.592
0.491
0.835
0.778
86.5
64.5
93.9
80.8
43.9
20.0
0.412
0.009
0.794
0.449
Accuracy measures were estimated using both resubstitution and 10-fold cross-validation techniques.
Table 3 – Representation of classifcation trees for the DESIGN and PURPOSIVE sampling surveys and lichen species
Variable type/name
L. oregana
DESIGN
Topographic
ASPE
ELEV
SLPE
Bio-climatic
ETPJA
ETPJD
MINDA
MINDD
PRECA
PRECD
RELHA
RELHD
SFMMD
SFMMA
TEMPA
TEMPD
VPAMA
VPAMD
Vegetation
BDLCNT
CNFCNT
FORBIO
VEGCNT
L. pulmonaria
PURPOSIVE
10
1,2,5,9,10
DESIGN
PURPOSIVE
P. anomala
DESIGN
P. anthraspis
PURPOSIVE
DESIGN
PURPOSIVE
8
8
4
6
6
10
5
3
5
3
8
8
8
7
2,4
3
1,2
2,11
3
6
6
6
4,6
7
4,6
1
5
3,9
9
1
3
2
9
1
3,5
1
3
4
2
2,8
4,7
7
5
7
7
4
6
7
5
2
7
4
1
4
3
1
6
7
9
3
2
8
2,5
3
7
3
Numbers represent the discrete levels in a tree, with higher numbers indicating splits further from the initial tree node. Empty cells indicate
the variable was not relevant to the classification tree model.
accuracy rates and the accuracy rates of the PURPOSIVE models evaluated on the EVALUATION data. In contrast, only 2 of 20
possible DESIGN tests indicated statistical difference between
the DESIGN cross-validation accuracy and the DESIGN models
evaluated on the EVALUATION data. Cross-validation accuracy
rates better reflected the true model accuracy than simple
resubstitution accuracy rates even though there were differences between the DESIGN and PURPOSIVE sampling forms.
4.
Discussion
Predictive statistical models are commonly used tools to estimate the likelihood of species presence (Edwards et al., 1996;
McNoleg, 1996; Frescino et al., 2001; Lawler and Edwards, 2002;
Moisen et al., 2006). These tools are essential for the ecological understanding, and management and conservation, of
plant and animal species. Levins (1966) was one of the first
to note that models must balance between the often competing wishes for generality in application and the specificity
desired for prediction. Best and Stauffer (1986), commenting
on bird-habitat relationship models, suggested that the specificity desired of predictive models is not likely to be achieved
given variability in time and space of both the response and
predictor variables. Van Horne and Wiens (1991) regarded an
ideal model as one that simultaneously maximizes ecological
realism, generality, and simplicity of use. Depending on the
objective of the study, one or two of the three is often sacrificed
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e c o l o g i c a l m o d e l l i n g 1 9 9 ( 2 0 0 6 ) 132–141
Table 4 – Percent correct classification (PCC), sensitivity and specificity accuracy rates, and kappa, for the DESIGN and
PURPOSIVE classification tree models of four lichen species in the Pacific Northwest, USA, evaluated on the independent
EVALUATION data
Species
Survey forms evaluated
Accuracy measure
PCC
Specificity
Sensitivity
Kappa
AUC
L. oregana
DES on EVAL
PURP on EVAL
z-Score
P
76.7
63.2
3.646
<0.001
87.3
76.8
3.383
<0.001
47.5
26.2
5.083
<0.001
0.368
0.032
4.600
<0.001
0.754
0.567
3.652
<0.001
L. pulmonaria
DES on EVAL
PURP on EVAL
z-Score
P
82.0
50.0
8.790
<0.001
92.2
46.1
14.106
<0.001
55.4
60.2
−1.192
0.233
0.514
0.048
6.698
<0.001
0.832
0.411
9.130
<0.001
P. anomala
DES on EVAL
PURP on EVAL
z-Score
P
85.0
56.0
8.214
<0.001
92.5
63.1
9.263
<0.001
54.2
27.1
7.030
<0.001
0.496
−0.076
4.712
<0.001
0.797
0.443
6.475
<0.001
P. anthraspis
DES on EVAL
PURP on EVAL
z-Score
P
81.7
67.7
3.996
<0.001
91.1
80.1
3.885
<0.001
46.9
21.9
6.681
<0.001
0.410
0.020
6.361
<0.001
0.781
0.517
4.832
<0.001
DES on EVAL, DESIGN on EVALUATION; PURP on EVAL, PURPOSIVE on EVALUATION, positive z-scores indicate higher accuracy rates for models
based on the DESIGN sampling survey; negative indicates lower rates.
at the expense of the others. From a conservation perspective,
where maximum prediction is often the goal, ecologists will
often sacrifice realism for model generality and usability.
Model generality and usability is assumed represented by
many different types of metrics (see Fielding and Bell, 1997), of
which resubstitution accuracy is one of the more common. In
our study, resubstitution accuracies were approximately the
same for the models built on the DESIGN and PURPOSIVE surveys, leading to the possible conclusion that both survey forms
led to models of similar utility. However, when evaluated on
the EVALUATION data, predictive accuracies were quite different, with the DESIGN outperforming the PURPOSIVE surveys.
Table 5 – Proportional tests comparing DESIGN and PURPOSIVE resubsitution accuracy rates vs. EVALUATION accuracy
rates for classification tree models built for four species of lichens in the Pacific Northwest, USA
Species
Accuracy rate
DESIGN
PURPOSIVE
z-Score
P
L. oregana
PCC
Specificity
Sensitivity
Kappa
AUC
4.447
4.052
5.024
3.971
4.066
<0.001
<0.001
<0.001
<0.001
<0.001
7.377
7.454
7.494
5.603
3.657
<0.001
<0.001
<0.001
<0.001
<0.001
L. pulmonaria
PCC
Specificity
Sensitivity
Kappa
AUC
2.414
0.793
4.173
2.084
1.489
0.016
0.427
<0.001
0.037
0.137
8.794
8.812
7.333
7.631
6.640
<0.001
<0.001
<0.001
<0.001
<0.001
P. anomala
PCC
Specificity
Sensitivity
Kappa
AUC
2.213
2.167
2.708
1.944
1.435
0.027
0.030
0.007
0.051
0.151
8.095
10.314
6.761
6.805
6.446
<0.001
<0.001
<0.001
<0.001
<0.001
P. anthraspis
PCC
Specificity
Sensitivity
Kappa
AUC
3.854
3.635
5.300
2.217
1.258
0.002
<0.001
<0.001
0.027
0.208
4.754
5.318
9.497
5.670
4.959
<0.001
<0.001
<0.001
<0.001
<0.001
Data for tests from Tables 2 and 4.
z-Score
P
139
e c o l o g i c a l m o d e l l i n g 1 9 9 ( 2 0 0 6 ) 132–141
Table 6 – Proportional tests comparing DESIGN and PURPOSIVE cross-validation accuracy rates vs. EVALUATION accuracy
rates for classification tree models built for four species of lichens in the Pacific Northwest, USA
Species
Accuracy rate
DESIGN
z-Score
PURPOSIVE
P
z-Score
P
L. oregana
PCC
Specificity
Sensitivity
Kappa
AUC
1.068
1.002
−0.536
0.000
−0.488
0.285
0.316
0.591
1.000
0.625
−5.321
−5.598
−3.942
3.300
0.607
<0.001
<0.001
<0.001
0.009
0.543
L. pulmonaria
PCC
Specificity
Sensitivity
Kappa
AUC
−0.308
−0.972
−1.374
−1.245
−1.228
0.757
0.331
0.169
0.213
0.219
−1.703
−4.707
3.710
−0.437
1.772
0.088
<0.001
0.002
0.662
0.076
P. anomala
PCC
Specificity
Sensitivity
Kappa
AUC
−0.942
−0.501
−3.619
−1.205
−0.708
0.345
0.616
<0.001
0.228
0.435
−4.373
−7.614
−0.528
2.902
1.695
<0.001
<0.001
0.597
0.004
0.089
P. anthraspis
PCC
Specificity
Sensitivity
Kappa
AUC
1.535
1.522
−2.822
−0.578
0.296
0.128
0.128
0.004
0.562
0.762
0.691
−0.263
3.118
−0.133
−1.233
0.489
0.792
0.002
0.894
0.217
Data for tests from Tables 2 and 4.
Clearly, the resubstitution accuracy estimates reported here
do not represent how poorly the models fit on the PURPOSIVE data perform compared to the models fit on the DESIGN
data. Moreover, the selected predictors from the classification
trees differed considerably between the DESIGN and PURPOSIVE surveys, leading to different ecological interpretations
as well. These differences in both model predictive generality and ecological interpretation should make modellers more
cautious in their interpretation than is currently observed in
the literature.
How representative our results are of other work is unclear
given the paucity of studies that have had the opportunity
to compare results using both resubstitution (training) and
independent test data sets. Fewer studies yet have evaluated
the differences in final model structures due to the underlying
probabilistic or non-probabilistic sampling designs that led to
collection of the training data. It is possible that some of the
differences between the classification trees fit on the DESIGN
and PURPOSIVE data sets could be due to sampling error,
or to some collinearity that remains among the predictor
variables even given our attempts to reduce collinearity. We
note, however, that variables strongly associated with the
presence (or absence) of lichen species consistently appear in
the classification trees, a result that would not be apparent if
either sampling error or collinearity were primarily determining the classification tree structures. This suggests that some
portion of the differences in model structure is due to the
underlying sample survey form. While these differences in
tree structures may have minimal impact on purely predictive
studies, they do have impact on the ecological interpretations
behind any model-derived distribution pattern (Austin et al.,
2006).
Even differences in the definition of what constitutes an
“independent” data set confound attempts to fully under˜
stand effects of sampling design on model accuracy. Munoz
and Felic´ısimo (2004), for example, defined as “independent”
the simple splitting of their original data into two subsets, one
for training and one for “independent” validation. Not surprisingly, differences in their reported prediction accuracies
between the 10-fold cross-validation and the 70:30 splitting
of their data for validation were minimal. This is because
any biases in the collection of the original data will naturally
carry through, no matter what type of randomization is
used to split the data, thereby precluding consideration of
the test data as truly independent. Such splitting does not,
in our opinion, constitute a truly “independent” evaluation, especially if the underlying sample survey was nonprobabilistic.
One seeming pattern is an observed decline in accuracies
from resubstitution to internal (e.g., cross-validation) and
external (i.e., independent) validation exercises. Fielding
and Haworth (1995) evaluated the generality of bird-habitat
models for three bird species in Scotland and documented
lower test than resubstitution accuracies. Other studies that
performed some type of internal validation of the training
data, whether jackknife or cross-validation, all show some
decline in resubstitution accuracies during the validation pro´
cess (see Frederick and Gutierrez,
1992; Martin and Morrison,
1999; Leathwick et al., 2006). We believe that for many types
of classification tools, including the classification trees used
here, resubstitution accuracy estimates alone are generally
poor estimators of true prediction accuracy rates. We further
suggest that resubstitution accuracy rates should not be
published in isolation if the ultimate intent of the model is
140
e c o l o g i c a l m o d e l l i n g 1 9 9 ( 2 0 0 6 ) 132–141
prediction, as they can lead to false impressions about model
usability.
Instead, we believe greater emphasis should be placed
on estimating accuracies through cross-validation techniques
(Fielding and Bell, 1997, Table 1) when it is difficult to perform
a truly independent evaluation (see Chatfield, 1995). For the
models fit on the DESIGN data, the 10-fold cross-validation
estimates of model accuracy were very good estimators of the
true predictive accuracies for the EVALUATION data. In the
two instances in which the cross-validated accuracies were
significantly different from the predictive accuracies for the
EVALUATION data, the cross-validation accuracy estimates
underestimated the true accuracies of the models. Similar
results comparing jackknifed accuracies against an independent data set were reported by Call et al. (1992). Accuracies
were similar between the jackknifed and independent data,
and both were lower than the resubstitution accuracies.
From a statistical perspective, non-probability sampling
efforts like purposive sampling can lead to bias in estimates
and uncertainty in the confidence about the estimate. This
does not imply that a purposive sample never represents the
population of interest. It does, however, cast doubt on how well
the sample represents the population, a concern when statistical models are used to address ecological questions like
species distributions or community structuring. In one such
example, Kodric-Brown and Brown (1993) replicated a study
by Glover (1989) on fish species in Australian desert springs,
correcting sampling biases due to incomplete sampling that
were acknowledged by Glover as inherent in the first study.
This correction led to completely different patterns of species
distribution and community structuring. Similarly, Austin and
Heyligers (1989) noted that failure to adequately sample across
the range of environmental variables influencing the distribution of plant communities can lead to erroneous conclusions
about species distribution patterns. In either circumstance,
attention to designs that minimize non-probabilistic biases is
paramount, yet it is unclear if ecologists fully appreciate the
magnitude of the biases that can arise when randomization
as an element of design is ignored and samples are collected
in a non-probabilistic manner.
Acknowledgments
The authors acknowledge the contributions of the following people in field collection, identification and data entry:
S. Berryman, M. Boyll, C. Derr, A. Ingersoll, D. Glavich, K.
Gossen, A. Mikulin, J. Riley, and R. Ulrich. Special thanks to P.
Halonen and B. Ryan (deceased) for help with difficult identifications, and to the many others who assisted with field
collections. Field work was funded by the PNW Region Air
Program and the Forest Service Survey and Manage Program.
We are also grateful for the assistance from a large number of individuals working on the Survey and Manage Program in the Pacific Northwest Forest Plan. Specifically, we
thank T. Brumley, N. Diaz, B. Rittenhouse, and N. Middlebrook
for guidance on Forest Service and Bureau of Land Management Survey and Manage Issues. Three anonymous reviewers,
and T.B. Murphy, helped improve the manuscript with their
insights. Funding was provided by the State of Oregon Bureau
of Land Management through a cooperative research arrangement with the USGS Forest and Rangeland Ecosystem Science
Center (FRESC), Corvallis, Oregon, and the USGS Utah Cooperative Fish and Wildlife Research Unit, Utah State University. The ideas behind this manuscript were developed during
the “2004 Generalized Regression Analyses And Spatial Predictions: Grasping Ecological Patterns From Species To Landscape” workshop held in Riederalp, Switzerland. The ideas
also benefitted from the liberal involvement of several excellent bottles of cognac.
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